Using a 5-minute and 8-minute hourglass timer, how can ypu measure 1 minute? explain using math and show the solution

To measure 1 minute using a 5-minute and an 8-minute hourglass, follow these steps:

1. **Start both hourglasses at the same time** (flip them both over simultaneously).
   
   - The 5-minute hourglass will run out of sand first (after 5 minutes), and at this point, the 8-minute hourglass will still have 3 minutes of sand left (since 8 - 5 = 3).
   
2. **When the 5-minute hourglass runs out**, flip it over immediately (so it starts again).

   - At this moment, the 8-minute hourglass will continue to run for 3 more minutes before it finishes.
   
3. **When the 8-minute hourglass runs out**, there will be 1 minute left on the 5-minute hourglass (because the 5-minute hourglass started at the same time and was flipped after 5 minutes).

4. **Wait for the remaining 1 minute** on the 5-minute hourglass to finish.

   - Once the 5-minute hourglass runs out again, exactly 1 minute has passed.

### Explanation:

- Initially, both hourglasses are flipped together.
- When the 5-minute hourglass finishes, 5 minutes have passed, and the 8-minute hourglass has 3 minutes left.
- Flipping the 5-minute hourglass at that moment allows us to measure the remaining 1 minute after the 8-minute hourglass finishes.

Thus, this process effectively measures **1 minute**.

---

### Relative questions:
1. Can you find a way to measure 7 minutes using these two hourglasses?
2. What is the shortest amount of time you can measure with both timers?
3. How would you measure 4 minutes using the same hourglasses?
4. Is it possible to measure 6 minutes with these hourglasses? How?
5. If you had a 3-minute and 9-minute hourglass, how would you measure 1 minute?

### Tip:
Using overlapping times from hourglasses is a clever method to measure smaller intervals.

Using a 5-minute and 8-minute hourglass timer, how can you measure 1 minute? Explain using math and show the solution.

Discover a step-by-step guide to measure 1 minute using 5-minute and 8-minute hourglasses. This solution uses the concept of overlapping time intervals and simple subtraction, ideal for middle school students learning about time and intervals. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation